Equipment Investment and the Relative Demand for Skilled Labor: International
Evidence
By

Karnit Flug
Zui Hercowitz

Working Paper 331

This paper investigates the effects of equipment investment on relative
wages and employment of skilled labor, using a panel data set which includes

a wide range of countries. This work is motivated by two alternative, not
mutually exclusive, hypotheses: equipment-skill complementarity and skill
advantage in technology adoption.
Complementarity between equipment and skilled labor is a hypothesis about
the production function: equipment and skilled labor are complements, while
equipment and unskilled labor are substitutes. Under this hypothesis,
equipment investment, by increasing the equipment stock, should generate a
higher relative demand for skilled labor. Using U.S. data, capital-skill
complementarity received empirical support in Griliches (1969), and since
then by others. Recently, Krusell, Lee, and Rios-Rull (1994) analyze
inequality in the U.S. using this property of the aggregate production
technology. Several related studies (e.g., Bound and Johnson 1992 and
Berman, Bound, and Griliches 1994) concluded that the major cause of the
large relative wage increase of skilled workers during the 1980s in the U.S.
was a shift in the skill structure of labor demand, brought about by
skill-biased technological change. Under the presumption that skill-biased
technological change is embodied in equipment, this mechanism is similar to
equipment-skill complementarity from this paper’s point of view.
Skill advantage in technology adoption is a related but different mechanism.
Assuming again that technologies are embodied in new equipment, this
hypothesis stresses a temporary productivity loss following investment,
which can be alleviated by the use of skilled labor. Bartel and Lichtenberg
(1987) find empirical support for this hypothesis. Grossman and Helpman
(1991) stress the mechanism of adopting (‘‘imitating’’) technologies
developed elsewhere. If technology adoption is a skill-intensive activity,
their model implies that technology adoption should be accompanied by an
increase the relative demand for skilled labor. The adoption process was
recently addressed in Jovanovic (1995), who stress the relative importance
of adoption costs over invention costs, and by Greenwood and Yorukoglu
(1996), who analyze the impact of investment-specific technological change
on the skill premium in a general equilibrium framework.
The impact of new equipment on labor market differentials is particularly
important for developing economies, such as some of the Latin American
countries undergoing a rapid process of privatizing and opening to
international trade. This process entails a massive investment in new
equipment, and hence potentially large differential effects on skilled and
unskilled labor demands. For example, Feenstra and Hanson (1995) found that
the relative wages of skilled workers in Mexico, particularly in industries
near the border with the U.S., have increased with trade liberalization.
They conclude that the large flows of direct investment had a dominant
effect in determining relative wages.
The focus of this paper is on the quantitative importance and dynamics of
equipment investment effects on labor market differentials, studied with
data on a wide range of countries.\footnote{%
Berman, Machin, and Bound (1995) also use a cross-country data set, and find
positive correlations between changes in employment of skilled workers in
manufacturing across industrial countries. Their presumption is that the
same technological changes must take place in many developed countries
within the same decade, leading to positive correlations if there is a skill
bias.} The analysis consists of panel regressions that address separately
the wage ratio and the employment ratio--obtained from different sources.
The wage ratio regressions include 37-39 countries and the employment ratio
regressions include 35 countries.\footnote{%

Within each panel, the sample periods differ for different countries--i.e.,
the panel data sets are unbalanced--with wage data ranging from the middle
1980s to 1992, and the employment data from the early 1970s to 1992.} Within
the present framework and available data, the two
hypotheses--equipment-skill complementarity and skill advantage in
technology adoption--are observationally equivalent, and hence we cannot
distinguish between the two.
The results suggest that investment in equipment raises the relative demand
for skilled labor, with relative wage responding after one year and relative
employment after three years. The wage response lasts for one to two years
only, while the employment response lasts at least six years. A one-year,
one-percentage point increase in the equipment investment/output ratio
raises the relative wage by six to seven percent with a lag of one year,
while the impact on relative employment after three years is about 15
percent, declining gradually thereafter.
The econometric specification is based on the assumption, discussed below,
that equipment investment is exogenous to relative (skilled/unskilled)
changes in wages and employment. Hence, the factors determining equipment
investment are not addressed here. One key factor is technological progress
specific to equipment, which was found in Greenwood, Hercowitz, and Krusell
(1996) to be the main source of growth in the postwar United States. Hence,
we view equipment-specific technological change as the fundamental source of
the effects studied here.
The paper is organized as follows. Section \ref{theory} addresses
theoretical considerations related to equipment-skill complementarity, and
Section \ref{econometric} discusses econometric considerations and the
estimation procedure. The alternative interpretation to the proposed
empirical equations, based on technology adoption, is addressed in Section
\ref{alternative}. Section \ref{data} describes the data sources, their
weaknesses, and the procedure adopted here to minimize those weaknesses. The
results are presented and discussed in Section \ref{results}, and Section
\ref{conclusion} concludes the paper.
\section{Theoretical considerations\label{theory}}
The basic premise in this section is complementarity between equipment and
skilled labor, and substitution between equipment and unskilled labor, i.e.,
a production function feature. Hence, the first basic element is the
aggregate production function
\begin{equation}
y_t^j=f(k_{et}^j,k_{st}^j,l_{1t}^j,l_{2t}^j;z_t^j), \label{pf}
\end{equation}
where $y_t^{j_{}}$ is output in country $j$ at time $t,$ $l_{1t}^j$ and $%
l_{2t}^j$ are the inputs of skilled and unskilled labor, respectively, $%
k_{et}^j$ is the stock of productive equipment, $k_{st}^j$ is the stock of
structures, and $z_t^j$ is an exogenous productivity shock. It is assumed
that there is no labor mobility across countries. The main assumption about $%
f(\cdot ),$ stated above, is that $f_{l_1k_e}>0$ and $f_{l_2k_e}<0.$ In
contrast, structures are hypothesized to complement both skilled and
unskilled labor. Specifically, $f_{l_1k_s}>0,$ $f_{l_2k_s}>0$ and $\partial
(f_{l_1}/$ $f_{l_2})/\partial k_s=0$ is assumed. A functional form
satisfying all these conditions is the CES formulation $f(\cdot
)=z_tl_{1t}^{\alpha _1}k_{st}^{\alpha _2}[\lambda k_{et}^{}+(1-\lambda
)l_{2t}^{}]^{1-\alpha _1-\alpha _2},$ $0<\alpha _1,\alpha _2,\lambda <1,$

studied by Krusell, Ohanian, and Rios-Rull (1994).
The second basic element is the evolution of equipment
\begin{equation}
k_{et}^j=k_e^j(i_{et-1}^jq_{t-1},\text{ }i_{et-2}^jq_{t-2,}...)
\label{keacc}
\end{equation}
where $i_{et}^j$ is gross equipment investment in consumption units--which
can be interpreted as the quantity of machines--and $q_t$ is an exogenous
variable indicating the worldwide state of the equipment technology at time $%
t$, satisfying $q_t>q_{t-1}$. The product $i_{et}^jq_t$ is therefore
equipment investment adjusted for technological improvement. This notion of
investment in efficiency units corresponds to {\it real investment }as
measured, in principle, by national income accountants. Equation (\ref{keacc}%
) incorporates the standard time-to-build assumption, i.e., there is a
one-period lag between the production of investment goods and the time in
which they become productive. The partial derivatives in (\ref{keacc}) are
positive and declining in value for higher lags, due to physical
depreciation. Hence, equations (\ref{pf}) and (\ref{keacc}) together imply
that real equipment investment with a lag of at least one period--i.e., $%
i_{et-1}^jq_{t-1},$ $i_{et-2}^jq_{t-2,}...$--by increasing the current stock
of productive equipment, has positive effects on:
\begin{itemize}
\item the skilled/unskilled wage ratio,
\item the skilled/unskilled employment ratio.
\end{itemize}
\noindent Lagged investment should have less of an effect as the lag
increases because of depreciation.
In a general equilibrium framework, the determination of equipment
investment, in consumption units, can be described by
\[
i_{et}^j=i_e(q_t,x_t^j)
\]
where $x_t^j$ is a country-specific vector of exogenous and predetermined
state variables. Accordingly, real investment is given by
\begin{equation}
I_{et}^j\equiv i_{et}^jq_t=i_e(q_t,x_t^j)q_t. \label{ie}
\end{equation}
Equation (\ref{ie}) says that real investment depends on the efficiency of
new investment goods and other exogenous variables. The main content of (\ref
{ie}) in the present context is that the variable $I_{et}^j$ represents both
the state of the technology $q_t$ and the extent to which country $j$
invests in this technology, $i_e(q_t,x_t^j).$ \footnote{%
See Cooley, Greenwood, and Yorukoglu (1995) for an analysis of technology
adoption, in which firms decide how much of the existing capital to replace.}%
The present context does not characterize the variables entering the vector $%
x_t$, except that they are exogenous or predetermined.\footnote{%
In this setup, investment at time $t$ involves capital goods of quality $q_t$
only, which, by assumption, is higher than that of previous vintages. A
richer framework would incorporate the possibility of investing in

previously existing technologies. For the present purposes, however, this
generality does not seem necessary. We return to this point below in
footnote \ref{latest}.}
\section{Econometric implications\label{econometric}}
\subsection{General considerations\label{general}}
The basic econometric strategy is to use panel data to estimate two
equations: one for the relative wage $w_{1t}^j/w_{2t}^j$ and the other for
the relative employment $l_{1t}^j/l_{2t}^j,$ both including the same set of
explanatory variables. As a preliminary step to motivate the actual
estimation, consider for a moment the hypothetical case where all the $x_t^j$
variables are observable. One could then estimate the equations as
\begin{center}
\[
w_{1t}^j/w_{2t}^j=\alpha _{wj}^{\prime }+\beta _{w1}^{\prime }\frac{%
I_{et-1}^j}{y_{t-1}^j}+\beta _{w2}^{\prime }\frac{I_{et-2}^j}{y_{t-2}^j}%
+...+\gamma _{w0}^{\prime }x_t^j+\gamma _{w1}^{\prime
}x_{t-1}^j+...+\varepsilon _{wt}^{\prime }
\]
and
\end{center}
\[
l_{1t}^j/l_{2t}^j=\alpha _{lj}^{\prime }+\beta _{l1}^{\prime }\frac{%
I_{et-1}^j}{y_{t-1}^j}+\beta _{l2}^{\prime }\frac{I_{et-2}^j}{y_{t-2}^j}%
+...+\gamma _{l0}^{\prime }x_t^j+\gamma _{l1}^{\prime
}x_{t-1}^j+...+\varepsilon _{lt}^{\prime }
\]
where $\alpha _{wj}^{\prime }$ and $\alpha _{lj}^{\prime }$ are
country-specific constants, the real investment variables $%
I_{et}^j=i_e(q_t,x_t^j)q_t$ are expressed as ratios to output $y_t$ to make
them comparable across countries, and the $\gamma $s represent
contemporaneous and lagged direct effects of $x_t^j$. The important point
here is that because of the presence of the lagged $x_t^j$ variables, the $%
\beta $s should capture the net effects of the technological development $%
q_{t-1},$ $q_{t-2},$..$.$
However, data that reasonably capture the relevant $x$s in the different
countries are not available, and hence, we cannot disentangle the pure
effect of technology from the other factors determining the extent to which
it is adopted. For this reason, the actual equations estimated are of the
type
\begin{equation}
w_{1t}^j/w_{2t}^j=\alpha _{wj}+\beta _{w1}\frac{I_{et-1}^j}{y_{t-1}^j}+\beta
_{w2}\frac{I_{et-2}^j}{y_{t-2}^j}+...+\gamma _w\widetilde{x}_t^j+\varepsilon
_{wt} \label{estw}
\end{equation}
\begin{center}
and
\end{center}
\begin{equation}

l_{1t}^j/l_{2t}^j=\alpha _{lj}+\beta _{l1}\frac{I_{et-1}^j}{y_{t-1}^j}+\beta
_{l2}\frac{I_{et-2}^j}{y_{t-2}^j}+...+\gamma _l\widetilde{x}_t^j+\varepsilon
_{lt} \label{estl}
\end{equation}
where $\widetilde{x}$ is a subset of $x.$ Lagged $\widetilde{x}$s are not
included given that the attempt to isolate the partial effects of the $q$s
is not pursued.\footnote{\label{latest}Because the empirical emphasis is
given to equipment investment, the question whether or not the technology
embodied in it is the latest seems unimportant. The main point is that the
equipment stock increases, leading to the effects mentioned in Section \ref
{theory}.}
The main prediction, according to the discussion in Section \ref{theory}, is
that the $\beta $s are positive and that their magnitudes decline with the
lags.
A relevant question at this point is whether an empirical relationship
between the relative labor market variables and lagged investment can be
generated by reverse causality, {\it in the absence }of equipment-skill
complementarity. To check for such reverse causality, let us consider the
econometric results that would obtain if movements in $w_{1t}^j/w_{2t}^j$
and $l_{1t}^j/l_{2t}^j$, due to exogenous relative demand (or relative
supply) shifts, are expected in advance. Given that the labor market
variables are ratios, an absolute {\it increase} in the demand for skilled
labor, for example, would be reflected in the same way as an absolute {\it %
decline} in the demand for unskilled labor. Hence, both absolute movements
are consistent with both higher and lower levels of expected economic
activity. Correspondingly, there should not be any systematic correlation
between wages and employmen {\it ratios }and $I_{et-1}^j$, $I_{et-2}^j$,...%
\footnote{%
There is an additional possibility of reverse causality {\it with }%
equipment-skill complementarity, where equipment investment reacts primarily
to the expected relative wage of skilled labor. Consider first a relative
supply shock of skilled workers. Given that this is expected in advance, $%
I_{et-1}^j$and $I_{et-2}^j,...$increase. Hence, shocks of this type would
lead to positive $\widehat{\beta }_l$s, but to {\it negative} $\widehat{%
\beta }_w$s, since higher lagged investments are accompanied by {\it lower }%
relative wages. Consider now an independent shock to the relative demand for
skilled workers. In this case the $\widehat{\beta }$s in {\it both}
equations would be {\it negative}, because investment would be reduced
(given the higher future cost of skilled labor) while relative wages and
employment increase. If both shocks coexist, one would accordingly expect
{\it negative }$\widehat{\beta }_l$s, while $\widehat{\beta }_w$s could be
of either sign. Hence, negative coefficients in the relative employment
equation would still be consistent with equipment-skill complementarity,
although obviously, that would invite a different formulation of the
equations.}
The following variables are selected for $\widehat{x}_t$:
\begin{itemize}
\item a time trend and per capita output, $y_t/pop_t,$ both representing
secular effects on both supply and demand for labor. They are intended to
capture the education level of the labor force, which, as a relative supply
shift, should have a positive effect on $l_{1t}/l_{2t}$ and a negative
effect on $w_{1t}/w_{2t}.$ They may also represent shifts in the skill
composition of output demand, which is likely to be towards skilled labor.

In this case the effects on both $l_{1t}/l_{2t}$ and $w_{1t}/w_{2t}$ should
be positive. Overall, we expect positive effects of time and $y_t/pop_t$ on $%
l_{1t}/l_{2t}$ but uncertain effects on $w_{1t}/w_{2t}.$
\item output growth, $\ln (y_t/y_{t-1}),$ representing current aggregate
shocks. No particular sign is predicted for the coefficient of this
variable, but given the likelihood of a positive correlation with equipment
investment, it seems appropriate to hold it constant, in order to isolate
the partial effects of equipment investment.
\end{itemize}
\subsection{Estimation procedure}
A panel data estimation routine with fixed country-specific constants is
used. In other words, all the slope coefficients are constrained to be the
same across countries, but specific factors not included in the $\widehat{x}$%
s are allowed in the country-specific constants.
\section{An alternative interpretation: skilled labor advantage in
technology adoption\label{alternative}}
Grossman and Helpman (1991, chapter 11) stress the mechanism of adopting
(‘‘imitating’’) technologies developed elsewhere.\footnote{%
In this model, the technology is developed in the ‘‘North’’ and imitated in
the ‘‘South’’.} If technology adoption is a skill-intensive activity, their
model predicts that technology adoption should be accompanied by an increase
in the relative demand for skilled labor. The empirical results in Bartel
and Lichtenberg (1987) are consistent with this hypothesis. They focus on
the labor market implications of technology adoption, estimating labor
demand equations which incorporate the average age of the equipment
stock--proxying for the average time since the introduction of new
technologies. They find a negative effect of this variable on the relative
demand for highly educated workers, supporting the hypothesis that adopting
equipment-embodied technologies increases the demand for skilled labor.
Note that the regression equations (\ref{estw}) and (\ref{estl}) above may
also be interpreted along the technology adoption lines. Under this
interpretation, the mechanism at work is not related to the production
function itself, but to the process of technology adoption--which requires a
high proportion of skilled labor. Correspondingly, the equipment investment
variables should have positive coefficients in both equations. Therefore,
the implications here are similar to those of the skill complementarity in
production, described in Section \ref{theory}. In a recent paper, Jovanovic
(1995) stresses the relative importance of technology adoption over that of
R\&D. The invention/adoption distinction highlights the similarity between
the implications of the technology adoption and the production function
considerations. In both cases, given the nature of the capital evolution
equation it should be the lagged investment variables which have important
effects on the labor variables. Current investment represents
contemporaneous production, while adoption starts only after the equipment
goods are incorporated into the capital stock. Both the adoption hypothesis
and the equipment-skill complementarity hypothesis imply that the impact of
equipment investment on labor market differentials, in terms of both wages
and employment, is a temporary one - the first because it refers to the
adoption period only, and the second because of depreciation, as discussed
in Section \ref{theory}. We discuss this point further in the concluding
section.

\section{The data\label{data}}
Three data sets are used: one for wages, another for employment, and a third
for investment and other macro data. Given the different forms in which the
wage and the employment data were constructed, the skilled/unskilled
classification is not the same for the two variables. We report below (at
the end of Section \ref{results}) some tests which suggest that the mismatch
may not be important for the results. The list of countries in the data set
appears in appendix, Table A1. The only criterion for including of a country
in each regression is that data for all the variables in that regression are
available.
\smallskip\
Wages:
\smallskip
The data are from the International Labor Organization (ILO) October
Inquiry, which is a worldwide annual survey. The October Inquiry, started in
its current form in 1983, is the only available detailed survey of wages by
occupation and industry for a large number of countries.\footnote{%
This data set was used previously by Freeman (1994).} The wage data cover 65
countries from all continents and all income levels. For most countries the
data cover the period from the mid 1980s through the early 1990s (about a
third of the countries have 5 years of data or less).
To minimize problems with the original data, we limited our coverage to
eight industries (mostly nonservices; see list in the Data Appendix). From
the different occupations reported for each industry we selected
‘‘laborers’’ as unskilled labor, and the rest of the occupations as skilled
labor. Given that only a few industries report professional occupations, we
defined skilled production workers as skilled labor. In the absence of
employment data by the same occupational classification, the averages across
industries are unweighted. First, average wages by skill levels within each
industry were used to compute the industry wage ratio, and then the ratios
across industries were averaged.
Whenever monthly wages were not reported, the hourly, daily, or weekly
figures were converted into monthly wages, using average hours worked--and
if not available, 40 hours per week were assumed. In some cases, only
contractual wage rates were available. Whenever both actual average earnings
and contractual wages were reported, actual earnings were used. In a few
countries and for some occupations, the wage provided was only for men or
only for women. For the rest it was the average for men and women. A
detailed description of the characteristics of the wage data by countries is
given in the appendix, Table A1. The specific countries entering the wage
ratio regressions and the corresponding sample periods are shown in Section
\ref{results} following the regression results.
\smallskip\
Employment:
\smallskip\

The employment data are from the ILO Statistical Database. They cover 52
countries over the period 1970 through 1993 (about 20 countries have data
only from the mid 1980s through the early 1990s). This database includes
economy-wide employment and unemployment by a broad occupational
classification. Skilled workers include professional, technical, and related
workers, and administrative and managerial workers. The unskilled category
is comprised of production and related workers, transport equipment
operators, and laborers, which are reported together. For this reason the
skilled/unskilled definition in the employment data differs from that used
in the wage data: the unskilled in our employment data include all
production workers, while in our wage data skilled production workers are
categorized as skilled.
We did not include a number of occupations - clerical and related workers,
sales workers, service workers and agriculture, animal husbandry, and
forestry workers - where the classification between skilled and unskilled
seems less meaningful in the present context. Given that these occupations
comprise most of the service and agriculture sectors, our definition of the
skilled/unskilled ratio is roughly parallel to that of
nonproduction/production workers used by Berman, Bound, and Griliches (1994)
for manufacturing only.
The list of countries entering the employment ratio regressions and the
corresponding sample periods are shown in Section \ref{results} following
the regression results.
\smallskip\
Macro data:
GDP and investment are from the Penn World Tables developed by Summers and
Heston (1991).
\section{Results\label{results}}
Basic results are addressed in subsection \ref{basic}, then the dynamics of
equipment investment effects are further analyzed in subsection \ref{lagged}%
, and subsection \ref{additional} reports an additional test, addressing
indirectly the mismatch in the definitions of skilled labor in wages and
employment.
\subsection{Basic Results\label{basic}}
We first address estimates of the wage-ratio equation and then estimates of
the employment-ratio equation, discussing the links between them.
Table 1 reports the results for the wage ratio equation under different
specifications. The regressions also include country-specific dummies, and
the $t$-statistics, in parenthesis, are computed using
heteroskedasticity-robust standard errors. These regressions include 37 to
39 countries, and, as shown in the countries list in Table 1a, the samples
vary across countries within the period from the middle 1980s to 1992.
Investment in machinery with a lag of one year,
the specifications positively and significantly
Column 2 reports a basic formulation with three
per capita--$YCAP$-- and a time trend--$YEAR$--

$IMACHY(-1)$, enters in all
at the one percent level.
additional variables: income
to capture long-run

developments, and GDP growth--$DY$-- to capture current aggregate shocks. $%
YCAP$ does not have a significant effect on the wage ratio. As discussed
above in subsection \ref{general}, this may reflect the offsetting effects
of a larger supply of skilled labor in more developed countries, and a
higher demand for skilled-labor intensive goods. The time trend represents
similar factors as $YCAP$, but stresses the time series aspect within each
country. The negative and significant coefficient suggests a high skill
premium at the beginning of the sample--the mid 1980s--and a decline over
time since then, probably reflecting a steady increase in the supply of more
educated workers. The coefficient of $DY$ is significant and negative. This
effect is consistent with the notion that unskilled labor demand, which is
likely to require little investment in specific human capital, is more
sensitive to short-run cyclical fluctuations. In contrast, hiring skilled
labor is likely to require specific training, and hence it would occur
gradually over time, as the economy permanently expands. This implies a
countercyclical behavior of both wage and employment ratios. The cyclical
behavior of the employment ratio is tested below in the context of the
coefficient of $DY$ in the employment-ratio equation.
The other columns check the robustness of the results in column 2, as well
as testing additional variables. The theoretical considerations in Section
\ref{theory} imply that only lagged equipment investments are relevant.
Column 3 tests this by also including current $IMACHY$. The coefficient is
insignificant, as the theory predicts. Equipment investment with a two-year
lag is introduced in column 4, but it also turns out to be statistically
insignificant. The coefficient and the $t$-statistic, though, are higher
than those of the current variable. Capturing effects of investment at
different lags is econometrically problematic given the strong
autocorrelation of the $IMACHY$ variable: 0.96 in the current sample. In
subsection \ref{lagged} below, we address the dynamics further.
Other investments relative to GDP, $OIY(-1)$, are included in column 5 to
test whether it is indeed machinery investment which has the positive
effect, or whether it is proxying for investment in general. The
considerations reviewed in Section \ref{theory} imply that $OIY$, which
includes other private as well as public investment, should have no effect.
Surprisingly, the coefficient turned out to be negative and significant,
suggesting complementarity between capital other than machinery and
unskilled labor.
Column 6 also includes an interaction term between machinery investment and
GDP per capita, to test whether the relative wage effects of equipment-skill
complementarity depend on the countryâ&#x20AC;&#x2122;s level of development. The negative
and significant coefficient of the interaction term indicates that the
relative wage response is weaker in richer countries. This result is
consistent with a higher supply elasticity of skilled labor in more
developed countries, which generates a smaller wage response to higher
skilled labor demand. The overall coefficient of equipment investment is
computed from column 6 as $14.6-0.59YCAP,$ which remains highly positive for
all countries in the sample.
Table 2 reports the same set of regressions as Table 1, but with the
employment ratio as the dependent variable. The number of countries here is
35. As Table 2a shows, the set of countries covered in these regressions
overlaps only partially with the set included in Table 1, and the sample
periods here are longer: they range from the early 1970s to 1992. The
coefficient of machinery investment is positive in all the specifications

except in column 4, which also includes $IMACHY(-2),$ and the significance
level is sensitive to the specification. These results, and particularly the
positive and significant coefficient of $IMACHY(-2),$ led us to check longer
lags. Running the basic specification (column 2 in Table 2) with an
increasing number of $IMACHY$ lags indicates that the strongest effect is
after three years: when $IMACHY(-3)$ is included, the other lags, including
the fourth, are insignificant. Hence, the employment ratio equations are
reestimated with $IMACHY(-3)$ replacing $IMACHY(-1),$ and reported in Table
3, on which we focus in what follows.
Column 2 reports the basic specification, with $IMACHY(-3)$ having a
positive and significant effect. The long lag until machinery investment
affects the employment ratio, along with the short lag for the effect on the
wage ratio, suggesting that the supply of skilled labor is inelastic in the
short run. Hence, when the equipment stock is enlarged--with a lag of one
year after machinery production--the increase in the relative demand for
skilled labor induces a higher skill premium immediately. Only with a lag of
two more years does the supply of skilled labor increase, either by formal
learning or by on-the-job training, leading to the delayed effect of
machinery investment on the employment ratio.\footnote{%
Note, however, that an increase in the relative input of skilled labor may
occur earlier by extending the number of hours per worker.} We return to the
dynamic effects of investment below in subsection \ref{lagged}.
The effect of other investment $OIY(-1)$ is negative and significant (see
column 3 in Table 3), as in the wage ratio equation. This strengthens the
impression of complementarity between other capital and unskilled labor,
suggested by the wage ratio regressions.
The positive and significant coefficient of $YCAP$ is consistent with both a
higher stock of human capital in higher-income countries (a supply effect),
and a higher demand for skilled labor-intensive goods (a demand effect), as
discussed earlier in the parallel context of the wage ratio. There, these
two effects offset each other, while here both increase the employment
ratio. $DY$ has a negative and significant effect, as it has on the wage
ratio, supporting the notion discussed earlier that unskilled labor demand
is more sensitive to the cycle than skilled labor demand. The time trend,
representing the within-country long-run demand and supply effects has, as
expected, a positive and significant coefficient. The interaction term
between investment in machinery and per capita income turns out to be
insignificant, while it should have been positive to be consistent with the
supply elasticity interpretation given to the negative coefficient in the
wage ratio equation. The insignificant effect of this term here, though, may
be related to its multicolinearity with $YCAP,$ which is very highly
significant in the employment regressions.\footnote{%
Deleting $YCAP$, the effect of the interaction term becomes positive and
highly significant, but the coefficient of the investment in machinery
itself becomes negative and insignificant. The total effect of investment in
machinery based on this regression ranges from -0.4 to 5.2, with 8 out of
the 35 countries included in the regression exhibiting a negative effect.}
\subsection{Lagged investment effects\label{lagged}}
As mentioned above, the $IMACHY$ autocorrelation is 0.96 in the relative
wage sample (in the relative employment sample the autocorrelation is 0.94).
Hence, capturing separate effects of subsequent lags is econometrically
difficult. Given that the dynamics are a key component in the mechanism

under study, the equations were reestimated with $IMACHY(-1),$ $IMACHY(-3),$
$IMACHY(-5)$, etc$.$ In this way, the problem of a strong correlation
between two subsequent investment variables is weakened and at the same time
longer dynamics are tested.
Table 4 reports the results. Columns 1 and 2 report the results for the wage
ratio without and with $OIY(-1),$ $OIY(-3),$ and $OIY(-5),$ and columns 3
and 4 correspond to the employment ratio. The results here are consistent
with basic ones above. The relevant machinery investment lags are short for
the wage ratio - only $IMACHY(-1)$ is significant, although $IMACHY(-3)$
also has a positive and quantitatively important coefficient. In contrast,
in the employment equation, columns 3 and 4, the first lag is insignificant,
while $IMACHY(-3)$ and $IMACHY(-5)$ are significant. Additional lags of up
to nine years were included and reported in column 5. $IMACHY(-7)$ turned
out to be significant but $IMACHY(-9)$ did not.
As mentioned above, the results suggest a very small elasticity of skilled
labor supply in the short run, but a larger elasticity in the longer run
(after at least two years). The dynamics following an $IMACHY$ shift can
then be described as follows. Investment has, once it is incorporated in the
equipment stock, a strong immediate impact on skilled relative wages, but
little effect on relative employment. Given higher wages, the relative
supply of skilled labor increases through learning, thereby lowering the
wage ratio and raising the employment ratio. This brings the relative wage
to the original level, but relative employment remains high for several more
years.
Quantitatively, a one-year, one-percentage point increase in the machinery
investment/output ratio raises the wage differential after a year by about
0.09, or 6.5 percent (the average wage ratio is 1.4). As mentioned above,
the effect thereafter is small and statistically insignificant. The
corresponding impact on relative employment can be judged by the sum of the $%
IMACHY$ coefficients, which equals 2.9 in column 5. Given that not all the
lags are included, one needs an additional assumption to identify the
year-by-year path of the coefficients. Assuming that starting from the third
lag (the first that is significant) the effect declines linearly, reaching
zero at the ninth lag, the resulting coefficients are 0.83, 0.69, 0,55,
0.41, 0.28, 0.14, and 0. This implies that a one-year, one-percentage point
increase in the machinery investment/output ratio raises the employment
ratio by 0.08, or by about 15 percent (the average employment ratio is 0.57)
after three years, with the effect declining gradually over six more years.
\subsection{An additional test\label{additional}}
As discussed in Section \ref{data}, the definitions of skilled and unskilled
labor in the wage and employment data are different. The mismatch is due to
the inclusion of skilled production workers in the skilled category for
wages, and in the unskilled category for employment. For two industries,
however, chemicals and electric light and power, wages of professional
occupations are available. Hence, the wage ratio of professionals to
laborers can be computed and used to test the change in wage ratio equation
results. The regressions using this wage ratio are reported in Table 5. The
results are qualitatively similar to those in Table 1. One difference is the
larger magnitude of the $IMACHY$ coefficients, which is consistent with a
monotonically increasing effect of machinery investment on labor demand by
skill levels. In other words, the demand effect is strongest on
professionals, weaker on skilled production workers, and weakest on laborers.

\section{Concluding remarks\label{conclusion}}
The evidence reported in this paper supports the hypotheses of
equipment-skill complementarity or skill advantage in technology adoption,
as manifested by a positive effect of machinery investment on the relative
demand for skilled labor. The results indicate an immediate response of the
relative wage of skilled labor and a delayed increase in relative
employment. This suggests that the supply of skilled labor is inelastic in
the short run, but reacts positively after a period of training. The present
results should be put in perspective by recalling that the wage and
employment data come from different sources, and differ in the respects
discussed earlier.
The present empirical formulation and data set do not make it possible to
distinguish between equipment-skill complementarity in production, and skill
advantage in technology adoption. The lack of a significant effect of the
current increase in the equipment stock (machinery investment with a lag of
one year) on the current relative employment of skilled labor does not seem
to support the need of skilled labor for technology adoption. However, it is
possible that the relative input of skilled labor does respond immediately
by an increase in hours per worker rather than in employment, given the time
involved in training new workers. (Our data set does not include hours per
worker.)
Investment other than in machinery has, surprisingly, a negative effect on
both relative wages and relative employment of skilled workers. This
suggests complementarity between other capital (private and public
structures) and unskilled labor. Studying the effects of more disaggregated
investment seems an interesting direction to pursue.
Time works in the direction of reducing wage differentials during the period
from the mid 1980s to the early 1990s, which is covered by the wage data.
This is a partial effect of time, which probably reflects high wage
differentials at the beginning of this period and an increase in the skill
level of the labor force during the period. Income per capita, which varies
dramatically across the countries in the sample, is very positively
correlated with relative employment of skilled labor, as one may expect, but
uncorrelated with the relative wage. The explanation we offer for these
results is that in higher income economies in both the relative supply and
the relative demand for skilled labor are higher, effects which cancel out
on the relative wage but work on relative employment in the same direction.
\newpage\
\begin{center}
DATA APPENDIX
\end{center}
Wages:
Source: ILO October Inquiry, years 1983-1994.
Simple averages of wage rates by occupation (disaggregation of 159
occupations) from the following industries:
1. spinning, weaving, and finishing textiles

2. printing, publishing, and allied industries
3. manufacturing of industrial chemicals
4. manufacturing of other chemicals
5. manufacturing of machinery
6. manufacturing of electronic equipment
7. electric light and power
8. construction
\smallskip\
Definitions of variables:
$WRATIO:$ average across industries of ratios of average wages of skilled
labor to average wages of unskilled labor. Skilled are professionals (a few
industries) and all production workers except laborers, and unskilled are
laborers.
$WRATIO1:$ average professional/laborers wage ratio of two industries:
industrial chemicals and electric light and power.
\smallskip\
Employment:
Source: ILO Labor Statistics Database.
Economy-wide data by broad occupational classification, excluding clerical
and related workers, sales workers, service workers, and agriculture, animal
husbandry, and forestry workers.
$ERATIO:$ ratio of employment of professional, technical, and related
workers + administrative and managerial workers to employment of production
and related workers, transport equipment operators, and laborers.
\newpage\
Macro data:
Source: Penn World Tables. Data are expressed in a common currency by using
purchasing power parities from the International Comparison Program of the
World Bank. See Summers and Heston (1991).
$YCAP:$ GDP divided by population.
$DY:$ annual growth rate of GDP.
$IMACHY:$ investment in machinery as a fraction of GDP.
$OIY:$ other investment (total investment less machinery investment) as a
fraction of GDP.